Journal
JOURNAL OF CHEMICAL PHYSICS
Volume 134, Issue 16, Pages -Publisher
AMER INST PHYSICS
DOI: 10.1063/1.3576141
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Funding
- U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering [DE-FG02-04-ER46108]
- Natural Sciences and Engineering Research Council of Canada
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We have previously shown that inverse statistical-mechanical techniques allow the determination of optimized isotropic pair interactions that self-assemble into low-coordinated crystal configurations in the d-dimensional Euclidean space Rd. In some of these studies, pair interactions with multiple extrema were optimized. In the present work, we attempt to find pair potentials that might be easier to realize experimentally by requiring them to be monotonic and convex. Encoding information in monotonic convex potentials to yield low-coordinated ground-state configurations in Euclidean spaces is highly nontrivial. We adapt a linear programming method and apply it to optimize two repulsive monotonic convex pair potentials, whose classical ground states are counterintuitively the square and honeycomb crystals in R(2). We demonstrate that our optimized pair potentials belong to two wide classes of monotonic convex potentials whose ground states are also the square and honeycomb crystal. We show that these unexpected ground states are stable over a nonzero number density range by checking their (i) phonon spectra, (ii) defect energies and (iii) self assembly by numerically annealing liquid-state configurations to their zero-temperature ground states. c 2011 American Institute of Physics. [doi:10.1063/1.3576141]
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